SPM Additional Mathematics Chapter 1 Functions

Additional Maths FUNCTION SMKBBSL_2010

1

PAPER 1(SET 1)

JOHOR 2009

1. Diagram 1 shows the graph of the function = + 1 , for the domain

2 5.

State:

(a) 1 5

(b) 3 [2 marks]

2. Given the functions 7 + 1 and

3 1. Find

(a) 1 8

(b) [4 marks]

3. Given the functions =3

2 and = 5 4 . Find . [3 marks]

KEDAH 2009

4. Diagram 2 shows the relation between set A and set B.

Diagram 2

(a) State the image of 9.

(b) Find the value of . [2 marks]


2

5. Given 1 3

5 , find the value of

(a) 3 ,

(b) if = 7. [4 marks]

6. Given that 2 + and 2: 9.

Find the value of and . [3 marks]

MELAKA 2009

7. Given function 7 2 and function 2 5.

Find :

(a) 1

(b) the value of 2 . [4 marks]

8. Given the function 3 + 2 and 2 + 1 , find the values of if

= 17. [3 marks]

MRSM 2009

9. Given that 2

4, 4, where and are constants and

1: 43

, 0, find the value of and . [3 marks]

10. Function is defined as

21+ 3,

1

2 and is a constant. Find the value

of such that only one image maps onto itself under function . [4 marks]


3

PAHANG 2009

11. Diagram 3 shows the relation between set P and set Q

Diagram 3

State

(a) the type of relation between set P and set Q.

(b) the value of if

2+ 1. [2 marks]

12. Given the function 3 1 , find

(a) the value of 2 4 , [2 marks]

(b) the function of if = 6. [2 marks]

PERAK 2009

13. Diagram 4 shows the graph of the function = 3 2 for the domain

3 4.

Diagram 4


4

State

(a) the value of ,

(b) range of corresponding to the given domain. [3 marks]

14. Given the function 2

+3. If =

3

2, find the value of . [2 marks]

15. Given the composite function = 32 5 and function = 2 2,

find 4 . [3 marks]

PERLIS 2009

16. Given that = 2, 1, 1, 2 , = 1, 4, 9 and the relation between set A and set B

is defined as the set of ordered pairs 2, 4 , 1, 1 , 1, 1 , 2, 4 .

State

(a) the range of the relation,

(b) the type of relation. [2 marks]

17. Given that 3 + 1 and 2

+3, 3, find

(a) 5 ,

(b) [3 marks]

18. Given that = 3 2 and = + 4, find

(a) 1 ,

(b) the value of if 1 2 = 4. [4 marks]

SABAH 2009

19. Given the function = 2 5 , find the value of 1 . [2 marks]

20. Given the function = 3 and composite function = 2 5, find the

function . [3 marks]

21. Given = 3 4 and 1 = + , find the value of and of .

[3 marks]


5

SARAWAK 2009

22. Diagram 5 shows a graph of the relation between two variables and .

Diagram 5

State

(a) the object of 8,

(b) the type of relation between and . [2 marks]

23. Given that the function = 2 + 5, = 2 4, find

(a)

(b) 2 [3 marks]

24. Given that the function : 3+2

5 , find

(a) 1

(b) the value of such that 1 = 3 [3 marks]


6

SELANGOR 2009

25. Given the function = 1 3 , for the domain 2 1,

(a) sketch the graph of the function on the axes in the answer space,

(b) state the range of corresponding to the given domain. [3 marks]

26. Given the functions 1 = 3 2 and = 3, find

(a) ,

(b) the value of , given 1 2 = 7 [4 marks]

27. Diagram 6 shows an arrow diagram that represents the function =

21,

Diagram 6

Find the value of

(a)

(b) [3 marks]


7

TERENGGANU 2009

28. Diagram 7 shows the function that maps to and the function that

maps to .

Diagram 7

Determine

(a) 1 6

(b) 4 [2 marks]

29. The functions and are defined by 1 3 and 2 + 3

Find

(a) 2 ,

(b) 1 2 [3 marks]

WP 2009

30. Diagram 8 shows the relation of set A and set B.

Diagram 8


8

State

(a) the image of 2

(b) the object that maps onto itself [2 marks]

31. Given that 7 3 and 2 .

Find

(a) 2 ,

(b) the possible values of , if 1 = 4. [4 marks]

32. Given the function =5

21,

1

2 and = 2 3.

(a) Find 1 .

(b) Hence, find . [4 marks]

KELANTAN 2009


Diagram 9

(a) State

(i) the value of ,

(ii) the range of the relation.

(b) Using the function notation, write a relation between set A and set B.

[3 marks]

34. Given the functions 3 + and 1: +4

3 , where and are

constants, find the value of and . [3 marks]


9

35. The following information refers to the functions and .

3 , where is a constant,

2+4

12

(a) Given that 4 = 10, find the value of .

(b) Find . [4 marks]


10

PAPER 1 (SET 2)

KELANTAN 2008


Diagram 10

State


(b) the range of the relation. [2 marks]

2. Diagram 11 shows the function

2 , 2, where is a constant.

Diagram 11

Find the value of . [2 marks]

3. The following information refers to the functions and .

3 2

6 + 1

Find 1 . [3 marks]


11

JOHOR 2008

4. Diagram 12 shows the relation between set P and set Q.

State

(a) the codomain of the relation,

(b) the type of the relation. [2 marks]

5. Given the inverse of function is 1: 7

2, 2,

(a) Calculate the value of 3 .

(b) State the value of where function is not defined. [3 marks]

6. Diagram 13 shows the function that maps set A to set B and the function that

maps set B to set C.

Diagram 13

Given = + 1 and = 2 + . Find the values of and .

[3 marks]


12

PERAK 2008

7.

Based on the relation defined by the ordered pairs {(3, 5), (3, 8), (5, 7), (5, 13)} , state


(b) the range of the relation. [2 marks]

8. Diagram 14 shows part of the mapping + 3.Find the values of [2 marks]

Diagram 14

WP 2008

9.

Based on the above information, the relation between R and S is defined by the set

of ordered pairs {(2, 6), (3, 8), (3, 10), (4, 12)}.

State

(a) the images of 3,

(b) the object of 12. [2 marks]

10. Function and are defined as 3 2 and 1

, 0, find .

[3 marks]

11. Given the function 3 and 1: 2 + where and are

constants, find the value of and of . [3 marks]

R = {2, 3, 4}

S = {6, 8, 10, 12}


13

KEDAH 2008

12.

Refer to arrow diagram above for the function : 3. Find the value of

(a)

(b) [3 marks]

13. Given : 3 2 and : 32 + 4. Find

(a) 1 2 ,

(b) . [4 marks]

14. Given that the inverse function of : 3 + is 1: 7

, find the value of

(a)

(b)

(c) 1 5 [3 marks]

PAHANG 2008

15. Two functions are defined by : 1 and : 2 + 3 + 1. Given that

: 2 + + , find the value of and of . [3 marks]

16. Given the function : 2 3 and : 8

, 0. Find 1 5 .

[3 marks]


14

17. Diagram 15 shows the linear relation f.

Diagram 15

(a) If the image of 6 is , state the value of .

(b) State the type of relation as shown in Diagram 15. [2 marks]

18. Given the function : 3

2, find

(a) the composite function 2, [2 marks]

(b) the inverse function, 1 . [2 marks]

19. Given the function = + 2 and = 2 + . If = 22 + 8 5,

find the value of and . [3 marks]

SABAH 2008

20. Given that 7 + 4. Find the value of if 2 = 5 + 3. [2 marks]

21. Given that 1: + 2, and = 3

2. Find the values of and .

[3 marks]

SELANGOR 2008

22. Given : 6

5 , find 4 . [2 marks]

23. Given the functions : + 3 and : 2 + 6 + 2. Find .

[3 marks]


15

24. In Diagram 16, set P is the domain and set Q is the codomain of a relation.

Diagram 16

(a) State the type of relation between set P and set Q.

(b) Using function notation, state the relation between set P and set Q

[2 marks]

SBP 2008

25. A function maps the elements from set P = 3, 4, 9, 16, 25 to

set Q = 0, 3, 8, 15, 24 as shown below in ordered pairs:

3, 0 , 4, 3 , 9, 8 , 16, 15 , 25, 24

(a) Write down the function notation for .

(b) State the value of

(c) State the codomain. [3 marks]

26. Given that function 3

, 0, and 1:

4

+, , find the value

of and . [3 marks]


16

TERENGGANU 2008


Diagram 17

State

a) the range of the relation

b) the type of relation [2 marks]

28. Diagram 18 shows the arrow diagram.

Diagram 18

Find

a) the value of

b) the object of -9 [2 marks]


17

MRSM 2008

29. A function is defined by : 3 +6

1, 1.

Find

a) the image of 2,

b) the object that has image 0. [3 marks]

30. Given the functions : 4 3 and : 162 24 + 14,

find the function . [3 marks]

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SPM Additional Mathematics Chapter 1 Functions